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Question

The tangent to the curve x = acos2θcosθ,y=acos2θsinθ at the point corresponding to θ=π6 is

A
parallel to the x-axis
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B
parallel to the y-axis
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C
parallel to line y = x
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D
None of these
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Solution

The correct option is A parallel to the x-axis
dxdθ = a cos 2θsin θ + a cos θ sin θcos 2θ= a(cos 2θ sin θ + cos θ sin 2 θ)cos 2θ = a sin 3θcos 2θ= dydθ = a cos 2θ cos θ a sin θ sin 2θcos 2θ = a cos 3θcos 2θ
Hence dydx=cot3θdydx|θ=π6 = 0
So the tangent to the curve at θ=π6 is parallel to the x-axis.

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